Abstract
Incidence spatial geometry is based on three-sorted structures consisting of points, lines and planes together with three intersort binary relations between points and lines, lines and planes and points and planes. We introduce an equivalent one-sorted geometrical structure, called incidence spatial frame, which is suitable for modal considerations. We are going to prove completeness by SD-Theorem. Extensions to projective, affine and hyperbolic geometries are also considered.
Resumen
La geometría espacial de incidencia está construida por medio de estructuras trisurtidas formadas por puntos, rectas y planos con relaciones binarias de interconexión, para cada dos de estos elementos. En este trabajo introducimos una estructura monosurtida, que denominamos marco espacial de incidencia y que resulta adecuada para un tratamiento modal. Probaremos la completitud del sistema por medio del SD-teorema. Las extensiones a los casos proyectivo, afín e hiperbólico son también considerados.
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Moyano, A.R., Rubio Ruiz, R.M. An axiom system for incidence spatial geometry. Rev. R. Acad. Cien. Serie A. Mat. 102, 237–249 (2008). https://doi.org/10.1007/BF03191824
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DOI: https://doi.org/10.1007/BF03191824